In: Economics
Suppose that people without jobs who were looking for work stop doing so. Other things the same, this makes
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 the labor force will remain the same and the unemployment rate falls  | 
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 both the labor force and the unemployment rate remains the same  | 
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 both the labor force and the unemployment rate fall  | 
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 the labor force will fall while the unemployment rate remains the same  | 
Labor Force = Employed + Unemployed
Unemployed are those who are willing and searching for work but does not find jobs. But here People without jobs have stop searching and thus will be considered as a discouraged workers and hence will not be considered as unemployed and hene will not be considered at be a part of labor force and hence Labor force will decrease.
Unemployment rate = (Unemployed/Labor force)*100
Now, Let initial number of unemployed = U and Labor force = L
Thus, Initial Unemployment rate = (U/L)*100
Let now A people stop searching and thus Labor force will decrease by A and also unemployed will also decrease by A(as discussed above)
=> New Unemployment rate = ((U-A)/(L-A))*100 (Note that ((X-Y)/(Z-Y)) < X/Z for all Y > 0)
Thus, New Unemployment rate < Initial Unemployment rate. So, unemployment rate will also decrease.
Hence, the correct answer is (c) both the labor force and the unemployment rate fall.